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We investigate the low-lying 2$^+$ states of $N=28$ isotones ($^{48}$Ca,$^{46}$Ar, $^{44}$S and $^{42}$Si) with using the canonical-basistime-dependent Hartree-Fock-Bogoliubov theory in which the pairing is takeninto account self-consistently. The quadrupole mode with very small excitationenergies emerges in $^{46}$Ar, $^{44}$S and $^{42}$Si due to the strongquadrupole correlations triggered by the quenching of the $N=28$ shell gap. Theimportance of the quadrupole correlations between the protons and neutrons, andthe role of the pairing correlation to reinforce the lowest 2$^+$ mode arediscussed. It is also shown that the $B$(E2$\uparrow$) values of $^{48}$Ca and$^{46}$Ar are plausibly explained by our calculations.

Quenching of N = 28 shell gap and a low-lying quadrupole mode in the vicinity of neutron-rich N = 28 isotones